What is the equation of a line perpendicular to y = -1/4 x + 8 and passes
through the point (0, 1)?

f(0) = 13

f(2) = -1

f(-2) = 19

f(1) + f(-1) = 24

for f(0): we will substitute x with 0 in the function

for f(2): we wil substitute x with 2 in the function

for f(-2): we will substitute x with -2 in the function

for f(1) + f(-1): we will find f(1) and f(-1) seperately, then we will sum the result

The value of the car after 8 years is $9,039.81

What is the Percentage?

Percentage, which is a relative figure used to denote hundredths of any amount. Since one per cent is equal to one-tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

As an illustration, 1% of 1,000 chickens is equivalent to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200. These relationships may be generalized as x = PT/100 where x is the amount equal to a certain percentage P of T and T is the total reference quantity selected to represent 100%. As a result, T is 1,000, P is 1, and x is determined to be 10 in the case of 1 percent of 1,000 chickens.

As we can see each year 10% of the actual value of a car the decrease

For example, $21,000 decreased to $18,900

21000-18000/21000 = 0.1x 100% = 10%

Next year

$18,900 decreased to $17,010

18900-17010/18900 = 0.1x100% = 10%

in 6th year the price will be

12400.29 - 1240.029 = $11,160.261

in 7th year the price will be

11,160.261-11,16.0261=$10,044.2349

in 8th year the price will be

10,044.2349-10,04.42349=$9,039.81

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Answer:

It is C  

Step-by-step explanation:  

Move all terms that don't contain x to the right side and solve.

Answer:

18months

Step-by-step explanation:

1424-560=864

864÷48=18

Answer:

18

Step-by-step explanation:

$1424-$560= $864

$864 divided by $48 = 18 months

Step-by-step explanation:

P = 8

Step-by-step explanation:

Given that P varies inversely with x then the equation relating them is

P = \frac{k}{x} ← k is the constant of variation

To find k use the condition P = 7 when x = 8 , then

7 = \frac{k}{8} ( multiply both sides by 8 )

56 = k

P = \frac{56}{x} ← equation of variation

When x = 7 , then

P = \frac{56}{7} = 8

The perimeter of triangle JKL is  determined as 68 units.

The perimeter of triangle JKL is calculated as follows;

The perimeter of triangle JKL is the sum of all the distance round the triangle.

Perimeter = length JK + length LK + length JL

AL = CL = 12

Length LK = CL + CK = 12 + 8 = 20

JA = JB = 14

KB = CK = 8

Length JK = JB = KB = 14 + 8 = 22

Length JL = JA + AL = 14 + 12 = 26

The perimeter of triangle JKL is calculated as;

Perimeter = 20 + 22 + 26

Perimeter = 68 units.

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Answer:

Here ,

sigma x=50+60+65+70+70+80+90=485

N=7

now,

Mean =sigma x÷N

=485÷7

=69.28

Answer:

D. Cannot be determined

Step-by-step explanation:

Similarly between given triangles can not be determined because given information are insufficient.

The correct option for the given triangles is D. Cannot be determined

Any two triangles will be considered as similar as they have congruent corresponding angles and the corresponding sides are in equal ratios.

Two shapes are Similar when one can become the other after a resize, flip, slide or turn.

Given are two triangle PWR and XYZ we need to determine whether they are similar or not,

So, we only have measurement of a pair of sides and measurement of an angle,

We have some similarity rules by which we can prove two triangles to be similar, they are :-

AA rule, Side Angle Side (SAS), Side Side Side (SSS) and Right-angle Hypotenuse Side (RHS)

Since, we do not enough information to conclude our discussion.

Hence, the correct option is D. Cannot be determined

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Answer:

a) 70 m

b) 35 m

c) 57 m

d) 500 m

e) 7.5 m

f) 57 m

Step-by-step explanation:

10 dm = 100 cm = 1 m.

1 dam = 10 m

1 km = 1000 m

100 cm = m

Correct ☑ ✔ Question :-

Transform in metre

a) 7 dam

b) 350 dm

c) 57000 mm

d) 0.5 km

e) 750 cm

f) 5.7 dam

a) 7 dam

1 dam = 10 m

so, 7 dam = 7 × 10 m = 70 m

b) 350 dm

10 dm = 1 m

so, 350 dm = 350/10 = 35 m

c) 57000 mm

1000 mm = 1 m

so, 57000mm = 57000/1000 = 57 m

d) 0.5 km

1 km = 1000 m

0.5 km = 1000 × 0.5 = 500 m

e) 750 cm

100 cm = 1 m

750 cm = 750/ 100 = 7.5 m

f) 5.7 dam

1 dam = 10 .

5.7 dam = 5.7 × 10 = 57 m

Answer:

8 is the hypotenuse.

sen(angle) = x/8

sen60 = x/8

0.87 = x/8

0.87·8 = x

x = 6.96

Answer:

£198

Step-by-step explanation:

£180 is 100%

10% of 180 is 180/10,

this is 18.

As it is a 10% increase you add that 18 onto 180 and you get 198.

The correct answer is option (c) 2.06.  For every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets

The asset-to-debt ratio for Blaine and Lindsay McDonald can be calculated by dividing their total assets by their total debt. Using the given values, the calculation would be as follows:

Asset-to-debt ratio = Total assets / Total debt

                   = $346,000 / $168,000

The asset-to-debt ratio is a financial metric that provides insight into the financial health and leverage of an individual, company, or entity. It measures the proportion of assets to debt and is used to assess the ability to meet financial obligations and the level of risk associated with the amount of debt.

In this case, Blaine and Lindsay McDonald have total assets valued at $346,000 and total debt of $168,000. By dividing the total assets by the total debt, we obtain the asset-to-debt ratio of approximately 2.06. This means that for every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets. A higher asset-to-debt ratio generally indicates a stronger financial position and lower risk, as there are more assets available to cover the debt obligations.

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The equation of the axis of symmetry for the given function is x = 1.

To find the equation of the axis of symmetry for the function f(x) = -4x² + 8x - 28, we can use the formula:

x = -b / (2a)

where "a" and "b" are coefficients in the quadratic equation ax² + bx + c.

In this case, a = -4 and b = 8. Plugging these values into the formula, we get:

x = -8 / (2*(-4))

x = -8 / (-8)

x = 1.

The axis of symmetry for a quadratic function in the form of \(f(x) = ax^2 + bx + c\)  can be found using the formula x = -b / (2a).

In the case of the given quadratic function f(x) = -4x² + 8x - 28, the coefficient of \(x^2\) is a = -4 and the coefficient of x is b = 8.

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An election system in which each state is divided into geographical regions (districts) and each district is represented by a single representative who wins by receiving the most votes even if it is not a majority is known as First-past-the-post (FPTP).

First-past-the-post (FPTP) is also known as simple majority system. Through this method of voting, the candidate with the most votes in the constituency is declared the winner of the election. This system is used in India in direct elections of Lok Sabha and State Assemblies. While FPTP is simple, it does not always allow for true representation, as a candidate can win despite getting less than half of the votes in a contest. In 2014, the National Democratic Alliance led by the Bharatiya Janata Party won 336 seats with 38.5% of the votes cast. Also, smaller parties that represent specific groups have less voting opportunities in the FPTP.

On election day, voters receive a ballot with a list of candidates. Since only one member of parliament will represent the region, each party has only one candidate to choose.

Voters put a cross next to their favorite candidate. But if they think their favorite has a low chance of winning, they can place a cross next to the one they like with the best chance of winning.

Being one candidate from each party, voters who support that party but do not like their candidate, either vote for the party they do not support or the candidate they do not like.

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Answer:

11.94

Step-by-step explanation:

In this problem you just need to add 6.74 with 5.2.

6.74 + 5.2 = 11.94

The correlation coefficient that best represents a moderate relationship showing fewer anxiety symptoms is a negative correlation coefficient.

In a negative correlation, as one variable increases, the other variable decreases. In the context of anxiety symptoms, a negative correlation would indicate that as one factor (e.g., a particular intervention, treatment, or activity) increases, the number or severity of anxiety symptoms decreases. This suggests a moderate relationship between the two variables, indicating that the higher the value of the independent variable, the lower the value of the dependent variable (in this case, fewer anxiety symptoms).

The correlation coefficient ranges from -1 to 1, with -1 representing a perfect negative correlation, 0 representing no correlation, and 1 representing a perfect positive correlation. A correlation coefficient close to -1, but not reaching -1, would be indicative of a moderate negative correlation and would best represent a moderate relationship showing fewer anxiety symptoms.

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$2,000 at 10% semi-annually becomes approximately $3,105.85, $1,000 at 12% monthly becomes $1,762.34, and $1,476.19 is needed to reach $2,000 at 8% quarterly.



To calculate the accumulated amount in each savings plan, we can use the formulas for future value (F) and present value (P). For the first savings plan, we have a deposit of $2,000 today at 10% interest compounded semi-annually. Using the formula F = P(1 + r/n)^(nt), where P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years, we substitute the given values to get F = $2,000(1 + 0.10/2)^(2*5) ≈ $3,105.85.

For the second savings plan, we deposit $1,000 today at 12% interest compounded monthly. Using the same formula, we get F = $1,000(1 + 0.12/12)^(12*5) ≈ $1,762.34.For the third savings plan, we need to find the present value (P) required to get $2,000 in 5 years at 8% interest compounded quarterly. Rearranging the formula to solve for P, we have P = F / (1 + r/n)^(nt). Substituting the given values, P = $2,000 / (1 + 0.08/4)^(4*5) ≈ $1,476.19.

Therefore, the accumulated amounts in the three savings plans over 5 years are approximately $3,105.85, $1,762.34, and $1,476.19, respectively.

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Answer:

No, you've already proven it's not irrational by writing it as 6/3.  You get 2.  

Step-by-step explanation:

An irrational number is any number that cannot be written as a fraction.

Answer:

y = 3x +26

Step-by-step explanation:

1. First find the slope. The formula for finding the slope is \(m=(y_{2}-y_{1})/(x_{2}-x_{1} )\).

\(m = (2-8)/(-8-(-6)) = -6/-2 = 3\)

2. Plug the slope value into the point-slope equation: y = mx + b.

\(y = 3x + b\)

3. In order to find b, plug one of the coordinates into the equation and solve for b.

\(2 = 3 (-8) + b\)

\(2=-24 +b\)

\(b = 26\)

4. Substitute the b value into the point-slope equation, and you will have

\(y=3x+26\)

I hope this helps!

Answer:

yes

Step-by-step explanation:

--

Answer:

This looks teacher made so i doubt you would be able to find this anywhere

Step-by-step explanation:

A)  The line integral over the straight-line path C1 is 1.

B)   The line integral over the curved path C2 is 1/5.

C)   The line integral over the path C3 ∪ C4 is 1/2.

a. The straight-line path C1: r(t) = ti + tj + tk, 0 ≤ t ≤ 1

We can calculate the line integral using the given path parameterization. Substituting r(t) into the vector field F, we have:

F = 2z i - x j + 2y k = 2t k - ti + 2t j

Now, let's calculate the line integral:

∫C1 F · dr = ∫C1 (2t k - ti + 2t j) · (dt i + dt j + dt k)

= ∫C1 (2t dt k - t dt i + 2t dt j)

= ∫[0,1] (2t dt k - t dt i + 2t dt j)

Since the dot product of i, j, and k with their respective differentials is 0, the line integral reduces to:

∫C1 F · dr = ∫[0,1] 2t dt k

= ∫[0,1] 2t dt

= [t^2] from 0 to 1

= 1 - 0

= 1

Therefore, the line integral over the straight-line path C1 is 1.

b. The curved path C2: r(t) = ti + t^2j + t^4k, 0 ≤ t ≤ 1

We can follow the same process as in part a to calculate the line integral:

F = 2z i - x j + 2y k = 2t^4 k - ti + 2t^2 j

∫C2 F · dr = ∫C2 (2t^4 k - ti + 2t^2 j) · (dt i + 2t dt j + 4t^3 dt k)

= ∫C2 (2t^4 dt k - t dt i + 2t^2 dt j)

= ∫[0,1] (2t^4 dt k - t dt i + 2t^2 dt j)

Since the dot product of i, j, and k with their respective differentials is 0, the line integral reduces to:

∫C2 F · dr = ∫[0,1] 2t^4 dt k

= ∫[0,1] 2t^4 dt

= [t^5/5] from 0 to 1

= 1/5 - 0

= 1/5

Therefore, the line integral over the curved path C2 is 1/5.

c. The path C3 ∪ C4 consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1)

We can calculate the line integral separately for each segment and then add them up:

For the line segment C3:

r(t) = ti + tj + 0k, 0 ≤ t ≤ 1

F = 2z i - x j + 2y k = 0i - ti + 2t j

∫C3 F · dr = ∫C3 (0i - ti + 2t j) · (dt i + dt j + 0k)

= ∫C3 (-t dt i + 2t dt j)

= ∫[0,1] (-t dt i + 2t dt j)

Since the

dot product of i and j with their respective differentials is 0, the line integral reduces to:

∫C3 F · dr = ∫[0,1] (-t dt i + 2t dt j)

= [-t^2/2] from 0 to 1

= -1/2 - 0

= -1/2

For the line segment C4:

r(t) = 1i + 1j + tk, 0 ≤ t ≤ 1

F = 2z i - x j + 2y k = 2t k - 1i + 2 j

∫C4 F · dr = ∫C4 (2t k - 1i + 2 j) · (0i + 0j + dt k)

= ∫C4 (2t dt k)

Since the dot product of i and j with their respective differentials is 0, the line integral reduces to:

∫C4 F · dr = ∫[0,1] (2t dt k)

= [t^2] from 0 to 1

= 1 - 0

= 1

Adding the line integrals over C3 and C4:

∫C3 ∪ C4 F · dr = ∫C3 F · dr + ∫C4 F · dr

= -1/2 + 1

= 1/2

Therefore, the line integral over the path C3 ∪ C4 is 1/2.

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Answer:

33.3

Step-by-step explanation:

tan A = opp/adj

tan 39° = 27/x

x tan 39° = 27

x = 27/(tan 39°)

x = 33.3

Answer:

y = mx + b is the slope-intercept formula

I use this formula a lot.

Hope this Helped! Have a GOOOOOOOOOD DAY!

Answer:

Dionne is correct

Step-by-step explanation:

x=1 y=x+1 for example: if x=33 y would = 34

The correct statement is " It is a function: y = x + 1 for all in the domain."

Option D is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

(1, 2), (3, 4), (5, 6), (100, 101)

We can make a  function.

y = mx + c

Now,

Take two ordered pairs.

(1, 2) and (3, 4).

And,

m = (4 - 2) / (3 - 1)

m = 2/1

m = 1

Now,

(1, 2) = (x, y)

2 = 1 x 1 + c

2 - 1 = c

c = 1

Now,

y = x + 1

So,

The relation is a function and the function is y = x + 1.

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The global maximum value is 44, and the global minimum value is -88.

To determine the global extreme values of the function f(x, y) = 11x - 5y subject to the given constraints, we need to analyze the function within the feasible region defined by the inequalities.

First, let's consider the boundary of the feasible region:

For x ≥ -8 and y ≥ x - 8, we have y ≥ -8 and y ≥ -x - 8. The feasible region is defined by the intersection of these two inequalities, which is a triangle with vertices (-8, -8), (-8, 0), and (0, -8).

For x ≤ 4 and y ≤ 4, we have y ≤ 4. The feasible region is the triangle with vertices (4, 4), (4, 0), and (0, 4).

Now, we need to evaluate the function at the vertices of the feasible region:

f(-8, -8) = 11(-8) - 5(-8) = -88 + 40 = -48

f(-8, 0) = 11(-8) - 5(0) = -88

f(0, -8) = 11(0) - 5(-8) = 40

f(4, 4) = 11(4) - 5(4) = 44 - 20 = 24

f(4, 0) = 11(4) - 5(0) = 44

From these evaluations, we can see that the maximum value of the function is 44, which occurs at the point (4, 0), and the minimum value is -88, which occurs at the point (-8, -8).

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Argument of the given complex number (-5√3 +  5i) will be 150°.

The argument of a complex number is defined as the angle inclined from the real axis in the direction of the complex number represented on the complex plane. It is denoted by “θ” or “φ”. It is measured in the standard unit called “radians”.

Argument of a complex number:

If a complex number if Z = (x + yi),

Imaginary part = y

real part = x

Argument of the complex number will be,

arg z = \(\text{tan}^{-1}(\frac{y}{x})\)

Given in the question,

Imaginary number 'z' = -5√3 + 5i

Imaginary pat 'y' = 5

Real part 'x' = -5√3

Therefore, arg z = \(\frac{y}{x}=\text{tan}^{-1}(\frac{5}{-5\sqrt{3} })\)

\(arg z = \frac{y}{x}=\text{tan}^{-1}(\frac{-1}{\sqrt{3} })\)

Since, tan is negative in IInd quarter,

arg z = (180 - 30)° = 150°

Therefore, argument of the given complex number will be 150°

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The argument of the complex number -5√3 + 5i is 150°.

The argument of a complex number is the angle between the positive real axis and the line connecting the origin to the complex number in the complex plane.

The complex number -5√3 + 5i can be written in polar form as rcos(θ) + irsin(θ), where r is the magnitude of the complex number and cos(θ) + isin(θ) is the complex number represented in polar form.

We can find the argument of - 5√3 + 5i by using the inverse tangent function to find the angle between the positive real axis and the line connecting the origin to the complex number in the complex plane. We can do this by dividing the imaginary part of the complex number by the real part:

arg(-5√3 + 5i ) = tan⁻¹(5 / (-5√3))

= tan⁻¹(-1/ √3)

= 150°

Therefore, the argument of -5√3 + 5i is 150 degrees.

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The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

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